
Accession Number : AD0660214
Title : MINIMUM CONCAVE COST SOLUTION OF LEONTIEF SUBSTITUTION MODELS OF MULTIFACILITY INVENTORY SYSTEMS.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
Personal Author(s) : Veinott,Arthur F. , Jr
Report Date : 15 OCT 1967
Pagination or Media Count : 57
Abstract : The paper shows that a broad class of problems can be formulated in terms of minimizing a concave function over the solution set of a Leontief substitution system. The class includes deterministic single and multifacility economic lot size, lot size smoothing, warehousing, product assortment, batch queueing, capacity expansion, investmentconsumption, and reservoir control problems in which all cost functions are concave. For such problems the optimum occurs at an extreme point of the solution set. The extreme points are characterized in each case by using the characterization of the extreme points of the solution set of a Leontief substitution system given in a companion paper. This approach enables most existing qualitative characterizations of optimal policies for inventory models with concave costs to be obtained in a unified manner. Dynamic programming recursions for searching the extreme points to find one that is optimal are given for a number of cases. The only algorithms given are those for which the computational effort increases algebraically (instead of exponentially) with the size of the problem. (Author)
Descriptors : (*INVENTORY ANALYSIS, MATHEMATICAL MODELS), (*MANAGEMENT PLANNING AND CONTROL, OPTIMIZATION), (*DYNAMIC PROGRAMMING, INVENTORY ANALYSIS), FUNCTIONS(MATHEMATICS), QUEUEING THEORY, THEOREMS, ALGORITHMS, MATRICES(MATHEMATICS), SET THEORY, COSTS
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE